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Nonlinear Modeling of Flexible Manipulators Using Nondimensional Variables

Chandra, Shaker and Ghosal, Ashitava (2006) Nonlinear Modeling of Flexible Manipulators Using Nondimensional Variables. In: Journal of Computational and Nonlinear Dynamics, 1 (2). pp. 123-134.

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This paper deals with nonlinear modeling of planar one- and two-link, flexible manipulators with rotary joints using finite element method (FEM) based approaches. The equations of motion are derived taking into account the nonlinear strain-displacement relationship and two characteristic velocities, $U_a$ and $U_g$, representing material and geometric properties (also axial and flexural stiffness) respectively, are used to nondimensionalize the equations of motion. The effect of variation of $U_a$ and $U_g$ on the dynamics of a planar flexible manipulator is brought out using numerical simulations. It is shown that above a certain $U_g$ value (approximately \geq 45 m/s), a linear model (using a linear strain-displacement relationship) and the nonlinear model give approximately the same tip deflection. Likewise, it was found that the effect of $U_a$ is prominent only if $U_g$ is small. The natural frequencies are seen to be varying in a nonlinear manner with $U_a$ and in a linear manner with $U_g$.

Item Type: Journal Article
Publication: Journal of Computational and Nonlinear Dynamics
Publisher: American Society of Mechanical Engineers (ASME)
Additional Information: Copyright of this article belongs to American Society of Mechanical Engineers.
Keywords: Nonlinear model;fexible manipulators; non-dimensional equations; system mode
Department/Centre: Division of Mechanical Sciences > Mechanical Engineering
Date Deposited: 25 Aug 2008
Last Modified: 19 Sep 2010 04:31
URI: http://eprints.iisc.ac.in/id/eprint/8291

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